How can I hang an object on a rope or cloth simulation
As no one could give a complete answer yet, I'll show you an easy hack/workaround that maybe is sufficient to solve your problem:

In my example I have filpped the plane, put it over the cube, made the cube a collision object, made the plane an unpinned cloth, let the cloth fall on the cube and wrap around it, found a keyframe in which the deformation was good, apply it as shape key, rotated back the plane so that the deformation was toward the bottom.

Then I animated the cube with 3 keyframes only: the start, the contact and the bouncing end; turned the second keyframe's interpolation form Beziers to bouncing, adjusted the values.

Then I went to the plane's shape key, set its max to 2 and min to -1, so tho have room for deformations in both directions, set manually a keyframe over every max and minimum of the bouncin curve, adjusted the curve in graph editor (there is more room to further adjust, but I think  it's enough for the tut purposes).

Ten minutes bouncin!